However, keep in mind that this can take a lot of work. Learning to sing on your own may require more work than working your voice with singing lessons or private singing tutorials. It's a lot like yoga or self-disciplined sports. You always have to develop patience, inner mental strength, breathing technique through listening to yourself, feeling yourself, and a good vocalist, because you have to approach all that even with a mentor.
I highly recommend Berklee Vocal for Performance with Donna McElroy DVD, and then some practice, and then some silence, and then some listening, and rinsing and repeating. A simple way to train your ear to tune is to play a song out loud. Choose a note you hear, pause the music and try to match the tone. You may be able to hear for yourself if you have matched the tone, but you can also record the music and your voice and play it back.
A simple way to train the ear (and also learn the vocal range) is to play a note on a piano and then try to match the pitch you hear.